%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP039-4 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:23:39 PM UTC 2026
% Result : Unsatisfiable 1.31s 1.73s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of clauses : 55 ( 26 unt; 7 nHn; 39 RR)
% Number of literals : 110 ( 6 equ; 49 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(a_times_c_is_d,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(total_function2,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(property_of_O2,axiom,
( product(X1,element_in_O2(X1,X2),X2)
| subgroup_member(X2)
| subgroup_member(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
cnf(closure_of_product,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-1.ax',closure_of_product) ).
cnf(prove_d_is_in_subgroup,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(b_is_in_subgroup,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
cnf(closure_of_inverse,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-1.ax',closure_of_inverse) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(identity_is_in_subgroup,axiom,
subgroup_member(identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_in_subgroup) ).
cnf(c_0_16,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_17,negated_conjecture,
product(a,c,d),
a_times_c_is_d ).
cnf(c_0_18,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_19,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2 ).
cnf(c_0_20,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_21,negated_conjecture,
( product(X1,c,X2)
| ~ product(X3,d,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_23,plain,
( product(X1,X2,X3)
| ~ product(X4,inverse(X2),X1)
| ~ product(X4,identity,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_24,plain,
( X1 = X2
| ~ product(X2,identity,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_26,axiom,
( product(X1,element_in_O2(X1,X2),X2)
| subgroup_member(X2)
| subgroup_member(X1) ),
property_of_O2 ).
cnf(c_0_27,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(X1,X2,X3) ),
closure_of_product ).
cnf(c_0_28,negated_conjecture,
( product(X1,c,d)
| ~ product(identity,a,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
~ subgroup_member(d),
prove_d_is_in_subgroup ).
cnf(c_0_30,plain,
( product(identity,X1,X2)
| ~ product(inverse(inverse(X1)),identity,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_31,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
product(b,inverse(a),c),
b_times_a_inverse_is_c ).
cnf(c_0_33,plain,
( subgroup_member(X1)
| subgroup_member(X2)
| product(X3,element_in_O2(X1,X2),X4)
| ~ product(X5,X2,X4)
| ~ product(X5,X1,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_34,negated_conjecture,
( ~ subgroup_member(c)
| ~ subgroup_member(X1)
| ~ product(identity,a,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_35,plain,
product(identity,X1,inverse(inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
subgroup_member(b),
b_is_in_subgroup ).
cnf(c_0_37,negated_conjecture,
( product(X1,inverse(a),X2)
| ~ product(X3,c,X2)
| ~ product(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( subgroup_member(c)
| subgroup_member(X1)
| product(X2,element_in_O2(X1,c),d)
| ~ product(a,X1,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_17]) ).
cnf(c_0_39,axiom,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
an_element_in_O2 ).
cnf(c_0_40,negated_conjecture,
( ~ subgroup_member(inverse(inverse(a)))
| ~ subgroup_member(c) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
closure_of_inverse ).
cnf(c_0_42,negated_conjecture,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_32]),c_0_36])]) ).
cnf(c_0_43,plain,
( X1 = X2
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_44,negated_conjecture,
( product(X1,inverse(a),multiply(X2,c))
| ~ product(X2,b,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_25]) ).
cnf(c_0_45,negated_conjecture,
( subgroup_member(c)
| subgroup_member(X1)
| ~ subgroup_member(X2)
| ~ product(a,X1,X2) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_38]),c_0_29]),c_0_39]) ).
cnf(c_0_46,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_47,axiom,
subgroup_member(identity),
identity_is_in_subgroup ).
cnf(c_0_48,negated_conjecture,
~ subgroup_member(inverse(a)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_49,plain,
( subgroup_member(multiply(X1,X2))
| ~ subgroup_member(X2)
| ~ subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_50,negated_conjecture,
( multiply(X1,c) = inverse(a)
| ~ product(X1,b,identity) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
subgroup_member(c),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]),c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( ~ subgroup_member(X1)
| ~ product(X1,b,identity) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
~ subgroup_member(inverse(b)),
inference(spm,[status(thm)],[c_0_52,c_0_18]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_41]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP039-4 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n002.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:18:31 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.31/1.73 % Version : CSE_E---1.7
% 1.31/1.73 % Problem : theBenchmark.p
% 1.31/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.31/1.73 % SZS output start CNFRefutation
% See solution above
% 1.31/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------